Trunking system



Patented Mar. 10, 1925.

UNITED STA-TES PAT-ENT oir-Fics.

HENRY M. ,BASCOILL O'E BROOKLYN, 4NEXT? YORK, IASSIGNOR, T0 -A`MERICAN TELEPHONE AND TELEGRAPH COMPANY, A CORPORATION 0F NEW YORK.

TRUNKING sYsrEivr.

vApplication filed February 26, 1921. Serial No. 448,020.

To all whom t may concer/rt:

Be itknown that I, HENRY M. Basooixi, residing at Brooklyn, in the county of Kings and State or' New York, have invented certain tems, of which the following isa speciiication. 7

This invention relates to signaling circuits and more particularly :to methods and means for trunking betweeircliiier'eiit subscribers` in a telephone exchange or between subscribers in diierent exchanges.

Heretofore in providing trunking arrangements for handling the traiiic originated by subscribers lines, particularly where the connections Awere established by means "of switching machinery, two general methods have been proposed. One method involved providing a sufficient number of trunks to handle all of the tratficoriginated by the subscribers lines involved and establishing connections between the calling subscribers lines and the trunks 'through a arrangement equipped with a` switching number of selecting points corresponding to the number of trunks necessary to handle the trailic. The other method consists in dividing the subscribers lines into groups and providing trunks for each group sutilcient in number to handle the traii'ic originating in the group.

The iii-st of these methods possesses the advantage that the total nuinberof trunks necessary to handle the traffic without an unduly large probability 'of a call being vlost due to all oi' the trunks being busy will be a minimum. The ymethod is subject lto the serious disadvantage, however, that each subscriber must have available a switching arrangement having a number of `switching terminals sutlicient to connect with each andV all of the trunks, and where the trailic is so large as to require a great number or trunks the expense involved in providing a switch` ing arrangement having the necessary capacity becomes prohibitive.

The advantage of the second method is that the subscribers groups may be` made sufficiently small so that the number of trunks necessary to handle the traliic originating in each group will be within the capacity limits of a relatively small vand inexpensive switching arrangement; that is,-

a switching arrangement having a compara- Improvements in Trunking Systively small number `of terminal points.

This method is subject to the disadvantage, however, that while econoinicin the matter or switching arrangementsr or machinery it is prodigal in the u'seoil trunks, since thel total number' of trunks required tovhandle4 the traiiic from all of the subscribers is greater than would 'be the case in the `irst method referred `to above, due to the factv that the ratio or' trunks to subscribers varies inversely with the number of subscribers having access to the trunks.

It is one of the principal objects of 'the present invention to yprovide a schemey for multiplying trunks such thatthe use' of switches having a small numberl of switching points will be permitted without requiring a large ratio of the total numberv of trunks to the total number of subscribers.

The above objects,lfas well as` other objects more fullyappearing hereinafter, are' accomplished by the use of `what is herein termed a"random slip multiple. The nature oi' this multiple will now be clear vvfrom the following description of the invention when read in "connection with the accomv panying drawings, Figure l of which is a schematic `diagrainof a so-called straight multiple, Figs. 2 and 3 yof which are schematic diagrams ofy trunking systems in which the multiple are slipped upon a purely random basis, while Fig. l is a schematic diagram oan arrangement yin which the slipping oit' the multiples is worked out in accordance with a deiinite rlaw which closely approximates the conditions involved in aperfect random slip.

Inforder to understand the principle lunderlying a"random slip multiple let us consider, for example, carrying the traiiic originated by subscribers? lines. Assume that each subscribers line is equipped with av 100 point selector, thereby giving each line access to the entire 10() trunks. vLet the order in which the "trunks are connected to the different selectors be varied as much as possible..k perfectly heterogeneous arrangement would be a group of 100 trunks n one suoli that when37 l(for example) of lthe y 100 trunks are busy a speciiied set of 37 trunks are as likely to be the trunks actually busy as any other set of 37 trunks.

"The arrangement so far described corresponds to the first method of trunking outlined above and has the advantages and disadvantages previously discussed. Let us now calculate for such a promiscuously connected multiple the probability that more than 20 terminals (for example) will have to be hunted over by a selector before an idle trunk is obtained. The load to be carried may be adjusted so that the probability comes out any desired value as, for eXample, .001. It is evident that under these conditions the last 80 terminals of every group maybe disconnected from the trunks without appreciably changing the eliiciency of the group of 100 trunks. Consequently each partially wired selector may be replaced by a 20 point switch having access to the same trunks in the same order as the first 2O trunks hunted over by the corresponding 100 point selector. Such an arrangement will involve what is herein termed a random slip multiple and has the obvious advantage that a 20 point switch may be used having access to 2O trunks previously selected at random from. the total number of trunks without increasing the total number of trunks required to handle the traino from all of the subscribers.

Considering the same arrangement from another view point, assume 5 independent groups of lines equipped with selectors. Let each group of selectors be wired to a group of 20 trunks. The total number of trunks required will therefore be 100; If we bring together these isolated groups of selectors and groups of trunks by a partial interchange of trunks, or in other words, by arranging matters so that each one of the 5 groups of selectors exchanges some of its trunks for some of the trunks assigned to each of the other 4 groups, We will have a promiscuously connected multiple of 10U trunks to some 2O of which each selector will have access. If this interchanging were done thoroughly the load carried by the total number of trunks with a given probability of lost calls would be appreciably greater than the load carried by the same number of trunks when divided into five isolated groups each of which is accessible to a 2O point selector.

In order that the advantages inherent in the random slip multiple may be more apparent a mathematical solution of the problem involved will now be given. lem may be stated as follows:

A group of T trunks handles the traiiic originated by n sub-groups of lines or switches.

Sub-group #l of lines or switches has access to a specified number t1 of the T trunks.

Subgroup #2 of lines or switches has access to a specified number t2 of the T trunks.

Some of these t2 trunks are not included in the t1 trunks assigned to sub-groups #1.

Subgroup :#:3 has access to a specified tu of the T trunks. Some of these t3 trunks are not included in the t1 trunks assigned to sub-group #l and some are not included in the t2 trunks assigned to sub-group #2. The trunks t1 and t2 together may, however, include all the t3 trunks.

Sub-group #n of lines or switches has access to a specified number zin of the T trunks. These tu trunks are not identical with either the t1, t2, t3 or tn l trunks but they are all included in the totality of t1+t2+ -l-tn-l trunks. v

Thus, no sub-group of lines or switches has the exclusive use of a set of trunks chosen from among the T trunks and on the other hand no two or more sub-groups use identically the same trunks.

It is not assumed above that numerically lzzzt I tn lzfn although this will probably be the case in practice.

Such a group of T trunks giving service to several over-lapping or inter-linking subgroups of lines, each of which sub-groups makes partial use of the T trunks, may be defined as a random slip multiple provided the following statement can be made with reference to it when S of the T trunks are busy they are as likely to be ont` specified set of S trunks as another specilied set of S trunks.

In order to solve this problem let Ptzprobability that a subscriber originating a call from a sub-group having access to t of T trunks fails to get an idle trunk.

Assume that at the moment the call is made S of the T trunks are busy. The probability of the existence of this assumed condition is The prob- .As e-L whereiA is the average load carried by the group T.

The probability that the assumed S busy trunks embrace the particular t trunks to which the subscr1ber under consideration has access 1s 'lherefore, the compound-probability that S trunks include the t trunks under con S ofthe'fl trunks are lbusy and-*that these sideration is f (At @l Arte-. (i/ S therefore, finally II have beenprepared toshoW the saving involved 1n a random I slip `multiple as compared Witlia straight multiple,

thatxis, a multiple in which the trunks are divided into independent groups, each group accessible to a switch having -a correspondingly small number' otterminal points.

In a system Where 2O pointV sender selec;

tors give' access to the senders. lof an auto` matie switching exchange the` saving .in

senders When the random slip arrangel mentis used instead of the straight. multiple Will'be as indicated in Table I. AIt can bev readily seen from .the table that With' the random slip arrangement the number of sende-rs required to carry a given load is considerably smaller than the number` of senders necessary for thek saine load vfiththe straight multiple. For example,

it i'svapparent'that if the Aallovvable probability ment for an average. load 015895, the expression "average. load being here takenl to mean the averageknumber of connections "existing at vanyone time for 'the entire group of lost calls yis .001 and the trunks are` divided into ten groupslofQO each the vranv doin slipy multiple arrangement will rethe straight multiple arrange [nrfr-baaw (LA).

ot trunks. The saving Vjust.referredtor yamounts to 31.5%.. On the otlierfhand., H

yin a case Where but one group is involved `and the average load'is 8.96,l 20senders Will.

be required in both.cases.and the random slip-multiple presents no `advantages .overNv straighty multiple as in this limiting case the random.slipinult1ple becomes a the straight multiple.

Table 'II shows -thesaving in inal-svvitchesf` which" would `result from a random are rangement oftrunks to finals in a panel 1 system Wheret-he lincomingyniultiple is divided into groups of 9A trunks each.l Here= also a sniallernumber of switches can,VV carry the same load as a larger number vvitli the ,straightv multiple.4 or inversely,` the v same number .of switches in the ment. i

` Table I.,

straightmumple. lg y Percent v Average load. l savngm i N b l. Total Total j senders.

fum e senders senders o groups' required. required.

i 2o 2o' 0 2 40' 34 15. 0 3 60 47 21.7 4 .80 60 25.0 100 -f 73 27.0 10 200 137- 31.5 300- 199 33. 7 400- randomrV arf, rangement can takeficare of ak largerload Table II.

mh straight multiple. ,Rngglfg l m. Per cent l Average load. savingu 1Vumber Total Total finals' 5' lf s finals finals l o group required. required. l

1 24 24 O 01 2 48 i3 10.4 3 72 60 16. 7 4 96 78 18.8 5 120 so 20, o 1 2i 24 0 4 2 is 4i l 14.0 i. 3 72 s. 20.@` l- 4 96 T 22. 9 58. 5 12o 25. o t

It is obvious, of Course, that multiple arrangements involving the random slip principle may be embodied in various forms. fn Figs. 2 and 3 are shown perfect random slips based on all of the 24C possiblepermutations of the numbers l, 2,

illustrate in schematic form the permutations of four trunks taken four at a time in accordance with the first method outlined at the beginning of this specification. In all. three figures a group of Tz-t trunks is shown, together with 01:24 sub-groups of subscribers lilies. Each sub-group is represented by one line equipped with a selector giving the line access t0 four trunks in the case of Fig. 1, three trunks in the case of Fig. 2 and two trunks in the case of Fig. 3. In Fig. 1 and the succeeding figures the arrows may therefore be taken to represent the wipers of the switches, cach of which is available to one or more subscribers and each switch having terminal points equal in number to the vertical lines connecting the arc of a circle representing` the contact points of the switch with t-he horizontal lines representing the trunks. The numbers below the arrows representing the wipers of the switch indicate the order in which the switches obtain access to the trunks.

If, in the case of the arrangement of Fig. 1 a determination is made of the probability that more than 3 terminals will have to be hunted over by a selector before an idle trunk isobtained, and it be found that this probability is within the allowable probability of lost calls, the connection leading to the last trunk selected by each switch may be omitted from the switches in Fig. 1, in which case we get the perfect random slip arrangement of Fig. 2, which is based upon permutations of e trunks taken 3 at a time.

Similarly, if it be found that the allowable probability will permit of dispensing with connections to the last two trunks selected by each switch in Fig. 1, we may obtain the perfect random slip multiple illustrated in Fig. 3 which involves permutations of 4 trunks taken two at atime.

3 ande, the pern'mtations being shown in Fig. 1, which The slip arrangements illustrated in Figs. 2 and 3 are based upon all possible permutations of the numbers involved. Consequently, each of these slips is a perfect random slip, since obviously no particular set of trunks is more likely to be busy than any other set involving an equal number of trunks. In practice` however, it would not be feasible to use slip arrangements based on all possible permutations, where the total number of trunks T is large. For example, a slip multiplel of T225 trunks, in which each line is equipped. with a :25 point selector, would require the lines to be divided into 25 21l 23 22 21:6,375,600 sub-groups if every possible permutation of 25 things taken 5 at a time is to appear.. It therefore becomes desirable to devise a system in which only a part of all of the pcssible permutations will be used and in which the selected permutations will be so chosen that no particular set of trunks is more likely to be busy than any other set involving the same number of trunks. In selecting a limited number of the total possible permutations, it is preferable to select a minimum amount of overlapping i.` e. permutations such that any trunk having a given number will appear in as few chosen permutations as possible.

Fig. el illustrates a practical form of slip arrangements obtained by following' the principles j ust discussed and in which a very thorough intermixture of trunks is attained without dividing the lines into an abnormal number of sub-groups. This figure shows what its herein termed a triangular slip arrangement in which T, the total number of trunks, is 15, and each selector is provided with five points. The first subgroup of lines to the left has assigned to it trunks numbered 1, 8, 6, 10 and 15, and the selector points corresponding to these points will be selected in the order stated. These particular numbers are technically known as triangular numbers, because they belong to the series of numbers which indicate the number of balls inv successive layers (counting from the top) in a triangular pile of cannon balls. The numbers of the trunks to be assigned tothe other groups are obtained by writing the numbers from 2 to 15 as the numbers of the first trunks to be selected by the groups to the right of that having assigned te it the numbers 1, 3, 6, 10 and 15. Similarly, the numbers of theA second set of trunks to be selected is obtained by writing successive numbers beginning with 4, while the third set is obtained Iby writing successive numbers beginning with l',etc In each instance, when the number 15 is reached, the succeeding number will be l. An analysis of this trunk arrangement shows that while it is not a perfect random slip arrangement, `it

conforms very closely to the requirements ofl the random slip multiple.

It will be obvious that the general process herein disclosed may be embodied in many other organizations Widely different from those illustrated Without departing from the spirit o' the invention as deiined in the following claims. t f

lVhat is claimed is:

l. A trunking system in which a plurality oit trunks are constructed 'for handling the traffic originating from all of the subscribers lines involved, the subscribers lines being divided into sub-groups, each having access to a number of trunks less than the total number involved, the trunks assigned to the several sub-groups being interchange'd so that the sub-groups overlap each other,

the order of selection of the trunks in the first sub-groups and the trunks assigned t0 said sub-groups being determined by the socalled triangular numbers 1, 3, 6, etc., and the trunks assigned to the said subgroups together With the order ot' selection of the trunks being determined by adding successive numbers to the numbers assigned to the first sub-groups.

2. A trunking system in which a plurality of trunks gives servi-ce to several overlapping and interlinked `subgroups of lines, each ksubgroup of lines'having access to a part only of the total number of trunks,

the'numbers of the trunks assigned to each sub-group being so chosen that the first subgroup will have assigned to it the so-called triangular numbers l, 3, 6 etc. and the other sub-groups Will have assigned to them the trunks Whose numbers are obtained by adding successive numbers to the numbers of the first sub-group.

3. A trunking system in which a plurality of trunks gives service to several overlapping and interlinked sub-groups of lines, each sub-group ot lines having access to a part only of the total number ot' trunks, the numbers of the trunks assigned to each subgroup and the order ot selection in eachparticular sub-group being obtained byassigning to the irst sub-group the so-called triangular numbers l, 3, 6, etc., and assigning to the remaining sub-groups numbers obtained by adding successive numbers to the numbers assigned to the first sub-group, whereby when a given number of the total number of trunks are busy, the probability of one set of trunks ofthe given number being busy, Will be substantially the same as the probability that any other set of equal number will be busy.

In vtestimony whereof, I have signed my -nameto this specification this 24th day oty February 1921.

HENRY M. BASGOM. 

